Melanie Bayley: Alice in Wonderland is a Parody of Nineteenth Century Math

[Melanie Bayley is a doctoral candidate in English literature at Oxford.]

SINCE “Alice’s Adventures in Wonderland” was published, in 1865, scholars have noted how its characters are based on real people in the life of its author, Charles Dodgson, who wrote under the name Lewis Carroll. Alice is Alice Pleasance Liddell, the daughter of an Oxford dean; the Lory and Eaglet are Alice’s sisters Lorina and Edith; Dodgson himself, a stutterer, is the Dodo (“Do-Do-Dodgson”)....

Yet Dodgson most likely had real models for the strange happenings in Wonderland, too. He was a tutor in mathematics at Christ Church, Oxford, and Alice’s search for a beautiful garden can be neatly interpreted as a mishmash of satire directed at the advances taking place in Dodgson’s field.

In the mid-19th century, mathematics was rapidly blossoming into what it is today: a finely honed language for describing the conceptual relations between things. Dodgson found the radical new math illogical and lacking in intellectual rigor. In “Alice,” he attacked some of the new ideas as nonsense — using a technique familiar from Euclid’s proofs, reductio ad absurdum, where the validity of an idea is tested by taking its premises to their logical extreme.

Early in the story, for instance, Alice’s exchange with the Caterpillar parodies the first purely symbolic system of algebra, proposed in the mid-19th century by Augustus De Morgan, a London math professor. De Morgan had proposed a more modern approach to algebra, which held that any procedure was valid as long as it followed an internal logic. This allowed for results like the square root of a negative number, which even De Morgan himself called “unintelligible” and “absurd” (because all numbers when squared give positive results)....

In Dodgson’s day, intellectuals still understood “temper” to mean the proportions in which qualities were mixed — as in “tempered steel” — so the Caterpillar is telling Alice not to avoid getting angry but to stay in proportion, even if she can’t “keep the same size for 10 minutes together!” Proportion, rather than absolute length, was what mattered in Alice’s above-ground world of Euclidean geometry....

The Cheshire Cat provides the voice of traditional geometric logic — say where you want to go if you want to find out how to get there, he tells Alice after she’s let the pig run off into the wood. He points Alice toward the Mad Hatter and the March Hare. “Visit either you like,” he says, “they’re both mad.”...

How do we know for sure that “Alice” was making fun of the new math? The author never explained the symbolism in his story. But Dodgson rarely wrote amusing nonsense for children: his best humor was directed at adults. In addition to the “Alice” stories, he produced two hilarious pamphlets for colleagues, both in the style of mathematical papers, ridiculing life at Oxford.

Without math, “Alice” might have been more like Dodgson’s later book, “Sylvie and Bruno” — a dull and sentimental fairy tale. Math gave “Alice” a darker side, and made it the kind of puzzle that could entertain people of every age, for centuries.